7.1
Weight and upthrust - why do some objects float in a fluid and others sink?
Why do objects float or sink in fluids?
When an object is partially or wholly
submerged in a fluid it experiences a force from all directions due to the
pressure of the fluid (gas or liquid).
This force acts at right angles to the
whole of the surface of an object.
Also, the pressure increases with
depth.
But, because pressure increases with
depth, an
object immersed in a liquid experiences a greater force at its bottom compared to the top
- this is illustrated in the diagram below of a solid block immersed in a
liquid.
The net
resulting force on the object, acting in
an upward direction, is called the upthrust an is equal to the weight of fluid
displaced.
Height (or depth) h2 corresponds to the higher pressure p2
at the greater depth at the bottom of the block.
Height (or depth) h1 corresponds to the lower pressure p1 at
a shallower depth at the top of the block.
The difference in height (depth) =
∆h, which corresponds to the difference in pressure ∆p.
Because of the difference in pressures,
the immersed object experiences a resultant force
upwards is called the upthrust - due to the higher fluid pressure at the
bottom of the object compared to the lower pressure at the top of the object.
The upthrust force is equal to the weight of the fluid displaced by the object
(see
the diagram above).
The displaced fluid equals the volume of
the object that is actually in the fluid - partially or completely
immersed in
the fluid.
If an object floats the weight of the
fluid displaced equals the weight of the object floating, which equals the
upthrust.
If an object sinks, its weight is greater
than the weight of fluid displaced, its weight is greater than the upthrust.
Water has a density of ~1000 kg/m3
and air has a density of ~1.2 kg/m3.
If the fluid upthrust is greater or
equal to the
weight of the object, then the object rises or
floats.
This is why a helium balloon floats and
rises in air. Helium is less dense than air (~0.18 kg/m3).
Our average density must be less than
water, because we can 'float'.
Porous balsa wood (density 340 kg/m3)
floats on water -
( see
'floating-sinking' experiments in section 7.2.)
If the weight of the object is greater
than the upthrust, then the object sinks
The object cannot displace enough fluid
to counteract its own weight, so it sinks.
and as a consequence, if the object has a greater density than the fluid, the
object sinks.
This is why a solid steel object (density
~8000kg/m3) like a fork, will sink in water.
Iron is much more
dense than water.
Brick and concrete objects have densities
of ~2200 kg/m3, so they sink in water.
SO, the deciding factor is the comparison of the
densities of the object and the fluid.
(i) If the density of the object is greater than
that of the fluid, it will sink to the bottom - complete immersion.
An object that is more dense that the
fluid it is placed in, cannot displace enough fluid to equal its weight.
Brick, iron objects are more dense than
water, so sink in it.
For objects more dense than the fluid, the weight of the object is
always larger than the upthrust and so it cannot float and will sink.
But beware, the shape of the object can
mean high density materials can float.
Iron is nearly eight times more dense than
water, but shape it into a boat and it floats.
This is because the boat shape
allows the displacement of water equal to the weight of the iron ship,
so it floats!
(ii) If the density of the object is
exactly the same as the liquid, the object neither moves up or down and will
float with its upper surface coincident with the surface of the liquid - wholly
immersed BUT floating.
I did find a block of wood with a density
of 1000 kg/m3, and it did exactly as predicted - see
'kitchen' experiment D.
(iii) If the density of the object is
less than the density of the fluid it is immersed in, then the object will float
upwards to the surface and some of the object will be above the surface of the
liquid - partial immersion.
An object that is less dense than the fluid
it is put in, weighs less than the volume of fluid equal to its own volume.
Consequently, the object can only
displace a volume of fluid equal to its own weight before it can be
completely submerged - so it floats because the objects weight is equal to
the upthrust.
Ice has density of 920 kg/m3
and floats on water (density 1000 kg/m3).
Ice sinks in petrol or diesel whose
densities are only 775 and 830 kg/m3 respectively.
You are used to the idea of objects floating in water, but helium balloons float
in air!
The weight of the helium balloon is far
less than the weight of the volume of air it displaces.
Therefore the upthrust from the air is
greater than the weight of the balloon which will rise - as you will have
observed as you see a 'freed' helium balloon rise high into the atmosphere.
Helium balloons are used by weather
scientists and weather forecasters to get information on the weather conditions
at high altitudes.
Since atmospheric pressure decreases with
height, the imbalance between the balloon's internal and external pressures
results in the helium balloon expanding.
Density is very important property to know
about a material, but shape of object is important too.
e.g. if the average density of an object
is less than that of water (~1000 kg/m3) it floats
if the average density of an object
is more than that of water it sinks!
In general: if the object has an
average density < fluid it floats and if the average density of the
object is > fluid it sinks.
Note the phrase 'average density' -
this is one way of explaining e.g. why a steel boat floats!
Because of the
shape of the boat, the average density of the boat (steel + contents +
air) is less than water.
Therefore the ship can displace a
volume of water equal to its weight, without sinking and can therefore
float.
This must be appreciated using
explanation is to do with upthrust and displaced of fluid as described
above.
Of course, if the boat develops a
leak, the less dense air is displaced by the more dense water and when the ship
fills up, due to the steel, the average density is greater than water
and the ship sinks!
See also
FORCES 6. Pressure in liquid fluids and hydraulic
systems
INDEX for physics notes: pressure,
forces, weight
and upthrust in fluids
Keywords, phrases and learning objectives for
upthrust in fluids - float or sink?
Be able to explain in terms of weight, density and
upthrust in fluids why an object might float
or sink in a fluid - in the context of an object in a liquid or gas.
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INDEX for physics notes: pressure,
forces, weight
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